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CHEN 4860 Unit Operations Lab
Design of Experiments (DOE)With excerpts from “Strategy of Experiments” from Experimental Strategies, Inc.
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The DOE Lab
Objectives – Help students be better experimenters through the methodology of modern experimental design, and the strategy of its application
Contents – Lecture, workshop, project Questions – No question is unimportant Resources – Slides, examples, instructor Benefits – ???
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DOE Lab Schedule
Wk of M T W R F
Apr. 3 DOE Lecture 1 DOE Lecture 1DOE Proposal due for M1, M2
groups
Apr. 10Review DOE
Proposals with M1, M2
DOE Lecture 2; DOE Proposal due for R1, R2
groups
Review DOE Proposals with
R1, R2
Apr. 17
Apr. 24Formal Memo due for M1, M2
Formal Memo due for R1, R2
Location & Time Txt 235 (3-5PM) AE 355 (1-2PM) Txt 235 (3-5PM)
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DOE Lab Schedule Details
Lecture 1 Introduction Workshop Fundamentals of
Strategy Factorial Design Redo Workshop
DOE Proposal Students develop
own written project proposal
Must be approved by Dr. Placek
Lecture 2 Work In-Class
Example Screening Designs Response Surface
Designs Formal Memo
Experimental plan Expected results Actual results Theory on differences Plan for further
experimentation
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Introduction
What is Experimentation?
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Objective of Experimentation
Improve process or product performance and yields
Improve product quality and uniformity Ensure your product (end-result) meets
your customer’s needs Ensure it ALWAYS does (Six Sigma) This is an ISO 9000 & above
requirement
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Five Stages of Experimentation
Design Data Collection Data Analysis Interpret Results Communicate Results
DESIGN One of the most important (and
often the most important) stages in experimentation
If you can see how the pieces should fit together, it is much easier to interpret and communicate your results.
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Experimentation Design
Objectives of the experiment Diagnosis of the environment Variables to be controlled Properties to measure Size of the effects to be detected Variable settings Number of experimental runs Carrying out the experiment Data analysis
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Obstacles to Experimenters
Belief that “ad hoc” methods work well
Lack of awareness of the advantages of “planning”
Hesitancy to use unfamiliar techniques
Lack of awareness of compromising conditions in the experimental situation
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Workshop
A typical R&D problem
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Problem Statement
Problem: R&D has developed a new resin. There is a problem. During start-up, the color of the resin, Y, has been too yellow. Retrospective data and chemistry suggest that yellowness probably is affected by three process factors, which are:
Factor Range of Variation
X1 Catalyst Concentration, % 1.00 to 1.80
X2 Reactor Temperature, oC 130 to 190
X2 Amount of Additive, kg 1.0 to 5.0
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Workshop Tasks
Where do you set the levels of the 3 process variables, X1, X2, and X3?
Support your findings with a description of the effects of the 3 factors on Y1 and draw a simple line chart
Describe strategy you used in your experiment
Boss’s best guess for a place to start is: X1 = 1.25 %, X2 = 137 oC, X3 = 3.0 kg
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Workshop Counter
Breakup into your M1, M2 and R1, R2 groups.
You have 15 min.
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Workshop Summary
What were the optimum set points for each variable?
What were the effects of each variable on the “yellowness” of the resin?
How many experiments did it take you to determine these results?
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Fundamentals of Strategy
What is experimentation strategy?
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Overall Strategy of Experiments
Minimize experimental error Maximize usefulness of each
experiment Ensure objectives of experiment are
met
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Minimize Experimental Error
High amounts of error in an experiment can make it extremely difficult (and time consuming) to interpret the results
In some cases, the error is so high that it is impossible to discern any influence the factors had on the response variable.
This could lead to a costly “redo” of the experiment.
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Experimental Error
Random Bias
Cause: Unknown Identifiable
Nature: Random Patterned
Management: ReplicationRandomization
& Blocking
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Random Error
Examples… Arrival at school when leaving home at
the same time and taking the same route
Readings from a platform chemical balance for the same sample
Continuous measurement often gives random error.
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Bias Error
Examples… Step Functions – a change in a shift, a
change in raw material or batch, a change in equipment, etc.
Cycles – a rhythmic variation due to weather, time of day, etc.
Drift – a deterioration of catatlyst, bearing or tool wear, etc.
Discrete measurement will often give bias error
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Managing Error
Random Error Ensure instruments are calibrated Replicate to take out the noise
Bias Error Block – estimate factor effects within
homogeneous blocks Randomize – convert bias error into
random error
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Maximize Usefulness of Data
To maximize the usefulness of data, put significant effort into the planning stage of the experiment
Both minimizing error and maximizing usefulness of the data will ensure the objectives of the experiment are met
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Planning the Experiment
Objectives of the experiment Diagnosis of the environment Variables to be controlled Properties to measure Size of the effects to be detected Variable settings Number of experimental runs Carrying out the experiment Data analysis
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Objectives of the Experiment
Set objective It should be specific, measurable, and have
practical consequence Determine the potential variables
Independent – Factors (X’s) Process variables and/or control knobs Must be influential, controllable, and
measurable Dependent – Reponses (Y’s)
Product yield, quality, and/or stability Can be more than one
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Diagnosing the Environment
Considering the objectives, level of knowledge, number of independent variables, and nature of independent variables, determine which type of experimental design to use.
ScreeningDesigns
Full FactorialDesigns
Response SurfaceDesigns
Many IndependentVariables
Fewer independent variables (<5)
“Crude”Information
Quality LinearPrediction
Quality non-linearPrediction
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Variables to be Controlled
Determine Properties (Effects) List of independent variables you wish
to measure Controlled Variables
List of other independent variables that affect the response variable that you wish to control
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Size of an Experiment
General Rules Must be large enough to detect factor
effects with necessary precision Must be small enough to conserve
resources Must be small enough to be timely
Set effect ranges accordingly Evaluate need for replication
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Factorial Design
Statistics in experimental design
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Factorial Design Overview
Factorial Design is one of many tools used in DOE
Pooling experimental error Determines significance of main effects Determines significance of interactions Evaluates variation contribution from
main effects
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Factorial Design (2k) K is number of factors 2 is number of levels (low, high)
X1
X2
X3
LO, HI, LO
LO, LO, LO
Pts (X1, X2, X3)
HI, LO, LO
HI, HI, LO
HI, LO, HI
HI, HI, HILO, HI, HI
LO, HI, LO
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+
Main Effects
Factor Effect = Y(+)avg – Y(-)avg “Hidden” Replicates: 4 runs at X2(+) and
4 runs at X1(-)
X2
-
X2effect = Y(X2+)avg – Y(X2-)avg
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Interaction Effects
“Hidden” Replicates: 4 runs at X1X2(+) and 4 runs at X1X2(-)
X2
+
X1X2 Interaction = Y(X1X2+)avg – Y(X1X2-)avg
-
X1
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Other Interaction Effects
X1*X2*X3 interactions work on same principle (X1X2X3(+)avg – X1X2X3(-)avg)
3 factor interactions are not common and are generally not significant
The exception to this rule is often interactions between chemical constituents
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One Factor at a Time (OFT)
No hidden replication Not space-filling No way to determine interactions
X1
X2
X3
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Factorial Design Tabular Form
Trial X1 X2 X3X1*X2
X1*X3
X2*X3
X1*X2*X3
1 - - - + + + -
2 + - - - - + +
3 - + - - + - +
4 + + - + - - -
5 - - + + - - +
6 + - + - + - -
7 - + + - - + -
8 + + + + + + +
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Significance of Effects and Interactions
If effects or interactions are significant, then they will be outside the variance of a normal curve
To determine the variance of the experiment Calculate the Stdev of the experiment
Se = sqrt(sum(Si2)/runs) Calculate the Stdev of the effects
Seff = Se*sqrt(4/trials)
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Significance of Effects and Interactions
To determine the variance of the normal curve, use Student’s t-test Estimate alpha as 0.05 for 95%
confidence. Estimate the degrees of freedom
degfree = (reps/run – 1)*(runs) Read the t statistic from table Calculate the decision limit
DL = t*(Seff)
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Significance of Effects and Interactions
If Si > DL, then effect is significant If not, move on.
-1.5 -1 -0.5 0 0.5 1 1.5
DL DL
E(X1) E(X2) E(X3)
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Significance of Variance
Replicate each run to learn which variables will reduce variation in the response variable Calculate the variance (Si2) of each run Calculate the average variance for the
high level and low level interaction (Si2(+)avg, Si2(-)avg)
Calculate the F statistic Fcalc = Si2avglarger / Si2avgsmaller
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Significance of Variance
To determine the two-tailed F statistic Estimate alpha as 0.10 Estimate the degrees of freedom as
degfree = (reps/run – 1)*(runs) Read the F statistic from table Evaluate F vs. Fcalc
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Factorial Example
Chemical Process Yield Improve process yield without knowing
reaction rates or chemical constituents Ink Transfer
Improve transfer of ink to industrial wrapping paper
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Factorial Design: Summary
Use the “cube” approach Set each factor as a dimension Code: Low = “-” and High = “+” Effects are comparisons of planes Hidden replication High-order interactions
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Workshop Redo
Using Factorial Design
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Workshop Tasks
Where do you set the levels of the 3 process variables, X1, X2, and X3?
Support your findings with a description of the effects of the 3 factors on Y
Describe strategy you used in your experiment
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Workshop Redo Counter
Breakup into your M1, M2 and R1, R2 groups.
You have 15 min.
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Workshop Redo Summary
What were the optimum set points for each variable?
What were the effects of each variable on the “yellowness” of the resin?
How many experiments did it take you to determine these results?
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Benefits Revisited
Maximize benefit/cost ratio of experiments
Improve productivity and yields Minimize process sensitivity to
variation (Maximize Robustness) Achieve better process design Shorten development time Improve product quality